Related papers: Twisted Permutation Codes
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
Traditionally, data compression deals with the problem of concisely representing a data source, e.g. a sequence of letters, for the purpose of eventual reproduction (either exact or approximate). In this work we are interested in the case…
A lower bound on minimum distance of convolutional polar codes is provided. The bound is obtained from the minimum weight of generalized cosets of the codes generated by bottom rows of the polarizing matrix. Moreover, a construction of…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.
We construct families of locally recoverable codes with availability $t\geq 2$ using fiber products of curves, determine the exact minimum distance of many families, and prove a general theorem for minimum distance of such codes. The paper…
Let $S_n^\lambda$ be the set of all permutations over the multiset $\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where $n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly…
Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empirically-found convolutional codes to label the trellis branches. This…
We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance…
We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse permutation there is exactly one valid way to assign…
We derive a simple lower bound for the multi-version coding problem formulated in [1]. We also propose simple algorithms that almost match the lower bound derived. Another lower bound is proven for an extended version of the multi-version…
This paper investigates the construction and analysis of permutation codes under the Chebyshev distance. Direct product group permutation (DPGP) codes, independently introduced by Kl\o ve et al. and Tamo et al., represent the best-known…
A permutation graph is the intersection graph of a set of segments between two parallel lines. In other words, they are defined by a permutation $\pi$ on $n$ elements, such that $u$ and $v$ are adjacent if an only if $u<v$ but…
In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…